immer_opcat: Estimation of Integer Item Discriminations

Description Usage Arguments Value Author(s) References See Also Examples

View source: R/immer_opcat.R

Description

Estimates integer item discrminations like in the one-parameter logistic model (OPLM; Verhelst & Glas, 1995). See Verhelst, Verstralen and Eggen (1991) for computational details.

Usage

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immer_opcat(a, hmean, min = 1, max = 10, maxiter = 200)

Arguments

a

Vector of estimated item discriminations

hmean

Prespecified harmonic mean

min

Minimum integer item discrmination

max

Maximum integer item discrimination

maxiter

Maximum number of iterations

Value

Vector containing integer item discriminations

Author(s)

Alexander Robitzsch <robitzsch@ipn.uni-kiel.de>

References

Verhelst, N. D. &, Glas, C. A. W. (1995). The one-parameter logistic model. In G. H. Fischer & I. W. Molenaar (Eds.). Rasch Models (pp. 215–238). New York: Springer.

Verhelst, N. D., Verstralen, H. H. F. M., & Eggen, T. H. J. M. (1991). Finding starting values for the item parameters and suitable discrimination indices in the one-parameter logistic model. CITO Measurement and Research Department Reports, 91-10.

See Also

See immer_cml for using immer_opcat to estimate the one-parameter logistic model.

Examples

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#############################################################################
# EXAMPLE 1: Estimating integer item discriminations for dichotomous data
#############################################################################

library(sirt)
data(data.read, package="sirt")
dat <- data.read
I <- ncol(dat)

#--- estimate 2PL model
mod <- sirt::rasch.mml2( dat , est.a = 1:I  , mmliter= 30)
summary(mod)
a <- mod$item$a		# extract (non-integer) item discriminations 

#--- estimate integer item discriminations under different conditions
a1 <- immer::immer_opcat( a , hmean = 3 , min = 1 , max = 6 )
table(a1)
a2 <- immer::immer_opcat( a , hmean = 2 , min = 1 , max = 3 )
a3 <- immer::immer_opcat( a , hmean = 1.5 , min = 1 , max = 2 )
#--- compare results
cbind( a , a1 , a2 , a3)

Example output

* immer 0.8-5 (2017-04-27 11:34:27)
- sirt 2.1-24 (2017-08-09 10:34:52)
------------------------------------------------------------
Semiparametric Marginal Maximum Likelihood Estimation 
Raschtype Model with generalized logistic link function: alpha1= 0  , alpha2= 0  
------------------------------------------------------------
...........................................................
Iteration 1     2017-09-29 13:06:50 
   Deviance = 3955.944
    Maximum b parameter change =  0.300852  
    Maximum a parameter change = 0.179056
...........................................................
Iteration 2     2017-09-29 13:06:50 
   Deviance = 3932.6605 | Deviance change = 23.283487
    Maximum b parameter change =  0.164255  
    Maximum a parameter change = 0.100263
...........................................................
Iteration 3     2017-09-29 13:06:51 
   Deviance = 3925.6262 | Deviance change = 7.03428
    Maximum b parameter change =  0.124258  
    Maximum a parameter change = 0.082788
...........................................................
Iteration 4     2017-09-29 13:06:51 
   Deviance = 3921.946 | Deviance change = 3.680179
    Maximum b parameter change =  0.105658  
    Maximum a parameter change = 0.08511
...........................................................
Iteration 5     2017-09-29 13:06:51 
   Deviance = 3919.6984 | Deviance change = 2.247649
    Maximum b parameter change =  0.102686  
    Maximum a parameter change = 0.089018
...........................................................
Iteration 6     2017-09-29 13:06:51 
   Deviance = 3918.092 | Deviance change = 1.606392
    Maximum b parameter change =  0.096286  
    Maximum a parameter change = 0.092055
...........................................................
Iteration 7     2017-09-29 13:06:51 
   Deviance = 3916.8161 | Deviance change = 1.27587
    Maximum b parameter change =  0.088139  
    Maximum a parameter change = 0.094079
...........................................................
Iteration 8     2017-09-29 13:06:51 
   Deviance = 3915.7459 | Deviance change = 1.070213
    Maximum b parameter change =  0.079338  
    Maximum a parameter change = 0.094998
...........................................................
Iteration 9     2017-09-29 13:06:51 
   Deviance = 3914.8286 | Deviance change = 0.917342
    Maximum b parameter change =  0.070573  
    Maximum a parameter change = 0.094797
...........................................................
Iteration 10     2017-09-29 13:06:51 
   Deviance = 3914.0385 | Deviance change = 0.790114
    Maximum b parameter change =  0.062257  
    Maximum a parameter change = 0.093529
...........................................................
Iteration 11     2017-09-29 13:06:51 
   Deviance = 3913.3596 | Deviance change = 0.678902
    Maximum b parameter change =  0.054618  
    Maximum a parameter change = 0.091315
...........................................................
Iteration 12     2017-09-29 13:06:51 
   Deviance = 3912.7791 | Deviance change = 0.580505
    Maximum b parameter change =  0.04776  
    Maximum a parameter change = 0.088317
...........................................................
Iteration 13     2017-09-29 13:06:51 
   Deviance = 3912.2853 | Deviance change = 0.493774
    Maximum b parameter change =  0.041703  
    Maximum a parameter change = 0.084717
...........................................................
Iteration 14     2017-09-29 13:06:51 
   Deviance = 3911.8673 | Deviance change = 0.41799
    Maximum b parameter change =  0.036412  
    Maximum a parameter change = 0.080695
...........................................................
Iteration 15     2017-09-29 13:06:51 
   Deviance = 3911.5149 | Deviance change = 0.352369
    Maximum b parameter change =  0.031827  
    Maximum a parameter change = 0.076416
...........................................................
Iteration 16     2017-09-29 13:06:51 
   Deviance = 3911.2189 | Deviance change = 0.295992
    Maximum b parameter change =  0.027872  
    Maximum a parameter change = 0.072011
...........................................................
Iteration 17     2017-09-29 13:06:51 
   Deviance = 3910.9711 | Deviance change = 0.247863
    Maximum b parameter change =  0.024464  
    Maximum a parameter change = 0.067586
...........................................................
Iteration 18     2017-09-29 13:06:51 
   Deviance = 3910.7641 | Deviance change = 0.206985
    Maximum b parameter change =  0.021529  
    Maximum a parameter change = 0.06322
...........................................................
Iteration 19     2017-09-29 13:06:51 
   Deviance = 3910.5917 | Deviance change = 0.172413
    Maximum b parameter change =  0.018995  
    Maximum a parameter change = 0.058964
...........................................................
Iteration 20     2017-09-29 13:06:51 
   Deviance = 3910.4484 | Deviance change = 0.143281
    Maximum b parameter change =  0.016802  
    Maximum a parameter change = 0.054854
...........................................................
Iteration 21     2017-09-29 13:06:51 
   Deviance = 3910.3296 | Deviance change = 0.118814
    Maximum b parameter change =  0.014897  
    Maximum a parameter change = 0.050922
...........................................................
Iteration 22     2017-09-29 13:06:51 
   Deviance = 3910.2312 | Deviance change = 0.098329
    Maximum b parameter change =  0.013237  
    Maximum a parameter change = 0.047175
...........................................................
Iteration 23     2017-09-29 13:06:51 
   Deviance = 3910.15 | Deviance change = 0.081229
    Maximum b parameter change =  0.011784  
    Maximum a parameter change = 0.043619
...........................................................
Iteration 24     2017-09-29 13:06:51 
   Deviance = 3910.083 | Deviance change = 0.066992
    Maximum b parameter change =  0.010508  
    Maximum a parameter change = 0.04026
...........................................................
Iteration 25     2017-09-29 13:06:51 
   Deviance = 3910.0279 | Deviance change = 0.055167
    Maximum b parameter change =  0.009384  
    Maximum a parameter change = 0.0371
...........................................................
Iteration 26     2017-09-29 13:06:51 
   Deviance = 3909.9825 | Deviance change = 0.04537
    Maximum b parameter change =  0.00839  
    Maximum a parameter change = 0.034133
...........................................................
Iteration 27     2017-09-29 13:06:51 
   Deviance = 3909.9452 | Deviance change = 0.037268
    Maximum b parameter change =  0.007509  
    Maximum a parameter change = 0.031356
...........................................................
Iteration 28     2017-09-29 13:06:51 
   Deviance = 3909.9146 | Deviance change = 0.030582
    Maximum b parameter change =  0.006727  
    Maximum a parameter change = 0.028767
...........................................................
Iteration 29     2017-09-29 13:06:51 
   Deviance = 3909.8896 | Deviance change = 0.025074
    Maximum b parameter change =  0.006031  
    Maximum a parameter change = 0.026354
...........................................................
Iteration 30     2017-09-29 13:06:51 
   Deviance = 3909.869 | Deviance change = 0.020541
    Maximum b parameter change =  0.00541  
    Maximum a parameter change = 0.024116
------------------------------------------------------------
Start: 2017-09-29 13:06:50 
End: 2017-09-29 13:06:51 
Time difference of 0.561682 secs
Difference: 0.561682 
------------------------------------------------------------
------------------------------------------------------------
sirt 2.1-24 (2017-08-09 10:34:52) 

Date of Analysis: 2017-09-29 13:06:51 
Time difference of 0.561682 secs
Computation time: 0.561682 

Call:
sirt::rasch.mml2(dat = dat, mmliter = 30, est.a = 1:I)

Semiparametric Marginal Maximum Likelihood Estimation 
Function 'rasch.mml2' 

Rasch Type Model with Fixed Discrimination, Guessing and Slipping Parameters 
alpha1= 0  alpha2= 0  
Moments: 
   M   SD  Var 
0.00 1.81 3.29 

------------------------------------------------------------
Number of iterations = 30 
Deviance =  3909.87  | Log Likelihood =  -1954.93 
Number of persons =  328 
Number of estimated parameters =  24 
AIC  =  3957.87  | penalty = 48    | AIC = -2*LL + 2*p  
AICc =  3961.83  | penalty = 51.96    | AICc = -2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC)
BIC  =  4048.9  | penalty = 139.03    | BIC = -2*LL + log(n)*p  
CAIC =  4072.9  | penalty = 163.03   | CAIC = -2*LL + [log(n)+1]*p  (consistent AIC)

Trait Distribution ( 21  Knots )
 Mean= 0 
 SD= 1 
 Skewness= 0
Item Difficulty Distribution ( 12  Items )
 Mean= -1.119  SD= 0.798 
Distribution of Items Administered ( 12  Items )
 Mean= 12  SD= 0 

EAP Reliability: 0.671
------------------------------------------------------------
Item Parameter 
   item   N     p      b est.b     a est.a thresh c est.c d est.d emp.discrim
1    A1 328 0.851 -2.013     1 1.028     1 -2.070 0     0 1     0       0.382
2    A2 328 0.738 -0.995     2 1.441     2 -1.434 0     0 1     0       0.549
3    A3 328 0.567 -0.312     3 1.132     3 -0.353 0     0 1     0       0.524
4    A4 328 0.460  0.206     4 0.858     4  0.177 0     0 1     0       0.450
5    B1 328 0.713 -1.651     5 0.597     5 -0.986 0     0 1     0       0.328
6    B2 328 0.506 -0.048     6 0.643     6 -0.031 0     0 1     0       0.352
7    B3 328 0.909 -2.399     7 1.164     7 -2.793 0     0 1     0       0.341
8    B4 328 0.683 -0.881     8 1.089     8 -0.959 0     0 1     0       0.483
9    C1 328 0.933 -1.733     9 2.972     9 -5.148 0     0 1     0       0.503
10   C2 328 0.713 -0.872    10 1.477    10 -1.288 0     0 1     0       0.585
11   C3 328 0.872 -1.585    11 1.805    11 -2.861 0     0 1     0       0.495
12   C4 328 0.735 -1.145    12 1.114    12 -1.276 0     0 1     0       0.464
   alpha1 alpha2
1       0      0
2       0      0
3       0      0
4       0      0
5       0      0
6       0      0
7       0      0
8       0      0
9       0      0
10      0      0
11      0      0
12      0      0
a1
1 2 3 4 5 6 
1 2 5 2 1 1 
              a a1 a2 a3
 [1,] 1.0282615  3  2  2
 [2,] 1.4409611  4  3  2
 [3,] 1.1318518  3  2  2
 [4,] 0.8584423  2  2  2
 [5,] 0.5974880  1  1  1
 [6,] 0.6427052  2  1  1
 [7,] 1.1644578  3  2  2
 [8,] 1.0891195  3  2  2
 [9,] 2.9715560  6  3  2
[10,] 1.4774742  4  3  2
[11,] 1.8048628  5  3  2
[12,] 1.1138202  3  2  2

immer documentation built on May 29, 2017, 10:07 p.m.